transitivity of a relation, through matrix.

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Is there a formula/algorithm to check whether any relation is transitive, using its matrix?

I seem to have found a formula $\sum_{i=1}^{n} \sum_{j=1}^{n} \sum_{k=1}^{n}$[ MTkj*(MTki-1)]=0

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Given such a logical matrix $A$, the square of the matrix $A^2$ shouldn't have non-zero in any place where $A$ has a zero.

See here: How to check whether a relation is transitive from the matrix representation?